Best of the West or best of the rest?

The NBA finals are right around the corner. Only a handful of games are left to be played in this 2013-2014 season, and homecourt advantage is still a hard fought battle for the top teams.

Miami wants it to increase their odds of winning a third straight championship, Indiana wants it to turn the tables if (more like when) it meets Miami in the Eastern conference finals and avoid a game 7 in Miami like it did last year, San Antonio wants it for the exact same reason except it lost to Miami in game 7 of the finals, and OKC wants it in case it faces Miami in the finals (plus it could provide Kevin Durant with an additional edge on the MVP race against LeBron James).

So yes, everyone wants homecourt advantage, it's been proved over and over again (including in this blog) that there is a definitive advantage to playing 4 games instead of 3 at home in the best-of-7 format. But how key is it really? Does homecourt advantage really determine the NBA champions? Do other factors such as the conference you are in or the adversity faced in the first rounds play a part?

Following on the tradition of the past years, the West is clearly better than the East. Consider this: right now, the Phoenix Suns hold the eighth-best record in the West with 46 wins and 31 losses, and has the last seed for the playoffs. But only two teams have a better record than that in the East, Miami and Indiana. Stressing to hold the last playoff spot in one conference versus a comfortable third seed in the other? Talk about disparity!

But if you had to guess whether the next champ was going to be from the East or West what would you say? That the eastern team would have an easier road to the finals, less games, less fatigue than their western counterpart? Or does evolving in a hyper-competitive bracket strengthen you, in a what-doesn-t-beat-you-makes-you-stronger argument?

Does the overall strength conference have an impact? Does the team with the best regular season record (and hence homecourt advantage) necessarily win? Does the team with the easiest path to the finals have an advantage?

To investigate this I've looked at all championships since 1990 (24 Playoffs) and looked in each case at some key stats for the two teams battling for the Larry O'Brien trophy, among these:

• number of regular season wins
• regular season ranking
• sum of regular season wins for opponents encountered in the Playoffs
• sum of regular season ranking for opponents encountered in the Playoffs
• number of games played to reach the Finals
• sum of regular season wins for all other Playoffs teams in their respective conferences
• sum of regular season ranking for for all other Playoffs teams in their respective conferences
• ...

So for Miami in 2013, the data would look something like:

• 66 regular season wins
• NBA rank: 1
• played 16 games before reaching the Finals
• 132 playoff opponent regular season wins (Indiana: 49, Chicago: 45, Milwaukee: 38)
• 38.5 playoff opponent regular NBA ranking (Indiana: 8.5, Chicago: 12, Milwaukee: 18)
• 320 playoff conference regular season wins (Indiana: 49, New York: 54, Chicago: 45, Brooklyn: 49, Atlanta: 44, Milwaukee: 38, Boston: 41)
• 84.5 playoff opponent regular NBA ranking (Indiana: 8.5, New York: 7, Chicago: 12, Brooklyn: 8.5, Atlanta: 14 Milwaukee: 18, Boston: 16.5)
• ...

As for the Spurs who were the other 2013 finalists, they had a worse record, emerged from a tougher conference and met stronger opponents while needing surprisingly less games to reach the Finals:

• 58 regular season wins
• NBA rank: 3
• played 14 games before reaching the Finals
• 148 playoff opponent regular season wins (LA Lakers, Golden State, Memphis)
• 27.5 playoff opponent regular NBA ranking (LA Lakers, Golden State, Memphis)
• 366 playoff conference regular season wins (Memphis, Oklahoma, Golden State, Denver, Houston, LA Lakers, LA Clippers)
• 51 playoff opponent regular NBA ranking (Memphis, Oklahoma, Golden State, Denver, Houston, LA Lakers, LA Clippers)
• ...

I then ran various models (simple logistic regression, and lasso logistic regression) to see how these different metrics helped predict who would win the champion come the Finals.

The conclusions confirmed our intuition:

• having more regular season wins that your opponent in the Finals provides a big boost to your chance of winning (namely by securing homecourt advantage, but the exact number of games provided a much better fit than a simple homecourt advantage yes/no variable)
• there were indications that having a tougher path to reach the finals (more games, tougher opponents) slightly reduced the probability of winning the championship, but none of those effects were very significant

The effect from difference in regular season wins can be seen on the following graph, where we have compared two (almost) identical teams evolving in identical conferences. The only difference between the two teams is the number of wins they've had in the regular season, shown on the x-axis. The y-axis shows the probability of winning the championship.

A five-game differential in wins will translate with a 73% / 27% advantage to the team with the most wins. Only a one-game advantage translates into a 55% / 45% advantage.

The conference effect appears quite minimal, and home-court advantage appears to be key. If Indiana hates itself right now for having let the number 1 seed in the East slip through its fingers, it can always try to comfort itself with the fact that (unless a major San Antonio / Oklahoma / LA Clippers break down occurs over the remaining games of the season), the Western team making it to the Finals would have held homecourt advantage no matter what.

It should also be noted that a "bad" conference isn't synonym of easy opponents. Just look how Brooklyn seems to have the Heat's number this year, the way Golden State had Dallas' in 2007 when it beat the number 1 seed in the first round. All season long the Golden State Warriors were the only ones who could match up against Dallas really well.

UPDATE: as of yesterday, Indiana has reclaimed the top seed in the East, but the final argument can be applied to Miami just as well. Whichever of these teams makes it to the Finals will face a tough opponent.

If you're the San Antonio Spurs...

I don't know about you, but I've found these NBA Playoffs to be more exciting than the last editions. Aside from Indiana-Atlanta (no offense), all first round match-ups had some backstory to them.
It got even better in the second round, the Bulls shocking the basketball world by stealing Game 1 against Miami, with Stephen Curry catching fire NBA-Jam-style in San Antonio. And then we get to conference finals, with buzzer-beaters to win games, crazy rallies and every other game going to overtime. The drawback of course is that I cut my life expectancy by three years due to the adrenaline rushs.

Okay, enough of the NBA advertising (I swear I'm not getting a dime from David Stern), what do the stats whisper as of today May 29th? Well, Spurs have some waiting to do until they figure out who their Eastern opponent is going to be...


Indiana or Miami in the Finals??

Tough choice if you've watched the last games, but the stats are oblivious to feelings, only hard facts matter, and the Heat remain a strong favorite, with almost 66% probability. Here's the probability breakout:

Winner	Number of Games	Probability
Miami	6	32.5%
Indiana	6	17.3%
Miami	7	33.1%
Indiana	7	17.1%

Spurs' 5th trophy?

As of today, here are the each team's probability of bringing the Larry O'Brien trophy home:

NBA team	Champion Probability
SAS	47.5%
MIA	39.6%
IND	12.9%

If Miami wins the series against Indiana, San Antonio's probability of winning it all drops to 39.8%:

Winner	num.games	prob
San Antonio	4	4.4%
Miami	4	7.8%
San Antonio	5	8.2%
Miami	5	17.6%
San Antonio	6	15.2%
Miami	6	15.5%
San Antonio	7	12.0%
Miami	7	19.3%

If Indiana wins the series against Miami, San Antonio's probability surges back to 62.5%:

Winner	num.games	prob
San Antonio	4	7.9%
Indiana	4	4.0%
San Antonio	5	18.9%
Indiana	5	7.3%
San Antonio	6	15.2%
Indiana	6	15.2%
San Antonio	7	20.4%
Indiana	7	11.1%

The big probability swing is of course due to the historical performance of both teams over the regular season and playoffs but also to the change in home court advantage: San Antonio has homecourt against Indiana, not against Miami.

So while San Antonio will not officially voice any preferences (and might even suggest Miami 'cause you're only considered the best if you beat the best), I can't help but feel that deep-down they got to hope for the unexperienced Pacers to end up against them on basketball greatest stage.

NBA: Spurs VS Thunder

Time for a playoff update now that the two contenders for the Western Finals are known.

Everybody wants to see Spurs VS Heat, but before then comes the Thunder hurdle, and despite the Spurs impressive performance up til now, this is definitely going to be a tough challenge.

The method is exactly the same from my previous post (which correctly identified Thunder beating the Lakers in 5 as the most likely scenario!). Entering the last numbers in the model, here's what came out:

Probability of Spurs winning the series: 55.6%

Series breakout:

Winner	Number of games	Probability
Spurs	4	6.6%
Thunder	4	5.3%
Spurs	5	15.8%
Thunder	5	9.5%
Spurs	6	14.3%
Thunder	6	16.9%
Spurs	7	19.0%
Thunder	7	12.7%

The three most likely scenarios are:
Spurs in 7 (19.0%), Thunder in 6 (16.9%) and Spurs in 5 (15.8%).

For the overall playoffs, the latest numbers suggests the West as championship favorites for now:

NBA team	Champion Probability
SAS	34.4%
OKC	25.7%
MIA	21%
BOS	12%
IND	4.6%
PHI	2.4%

Verdict in the upcoming weeks!

Who will be the 2012 NBA champs?

As of today, and after a shortened but game-packed season, the 2012 NBA playoffs are finally underway!

Let's take a look at the playoff bracket:

Some very interesting match-ups ahead!

But in addition to trying to catch as many games as possible, I also wanted to take a stab at predicting who would become the 2012 NBA champions of course!

Just as in the previous posts, I will start off with a very simple model and work from there to improve its reliability.

So, what simple model can be establish to predict the outcome of the match-up between two teams? Let's simply consider the number of victories they obtained during the course of the season and derive a probability of winning a game from there.

Let us assume team 1 won 50 games and team 2 won 40 games. I would then grossly estimate that team 1's probability of winning a game against team 2 is 50 / (50 + 44) ~ 56%.

Similarly to many other sports, each match-up is a best-of-seven, meaning that the first team to win 4 games gets to advance to the next round. Therefore, if team 1 has a probability p of winning a game against team 2, team 1's probability of winning the match-up is:

P(win match-up) = p⁴ (1 + 4 * (1 - p) + 10 * (1 - p)² + 20 * (1 - p)³)

Indeed, team 1 needs to win 4 games hence the p^4, and team 2 can win anywhere from 0 to 3 games with probability (1 - p). Depending on the number of games team 2 wins, the number of arrangements varies, yielding the 1, 4, 10 and 20. In the previous example, team 1 has an overall probability of winning the series of 62%, despite having won 25% more games during the season. This very simple framework can help explain the many upsets that are regularly witnessed.

So now that we can figure out the probability of team 1 winning its first match-up, we can go to the next step and figure out the probability that will win the series against the winner of the team 3 - team 4 match-up:

P(team 1 wins second round) = P(team 1 beats team 3) * P(team 3 beats team 4) + P(team 1 beats team 4) * P(team 4 beats team 3)

I started this script this morning when none of the games had been played yet, and obtained the following probabilities for each team of becoming the NBA champions:

NBA team	Champion Probability
CHI	15.0%
SAS	14.4%
OKC	11.3%
MIA	10.5%
IND	6.7%
LAL	5.8%
MEM	5.4%
ATL	5.0%
LAC	4.7%
BOS	4.3%
DEN	3.7%
ORL	3.3%
NYK	2.7%
DAL	2.6%
UTA	2.4%
PHI	2.2%

I re-ran the script after the results of today's first four games (good thing I'm single) and obtained the following similar results:

NBA team	Champion Probability
CHI	17.9%
OKC	14.1%
SAS	13.6%
MIA	13.0%
LAL	5.2%
MEM	5.0%
ORL	4.5%
ATL	4.4%
LAC	4.4%
IND	4.1%
BOS	3.8%
DEN	3.4%
UTA	2.2%
NYK	1.6%
DAL	1.5%
PHI	1.2%

Winning the first game did bump up the teams by a couple of percentage points, Oklahoma City now pulled in front of San Antonio.

But wait! Before you run to the closest sports betting bar to put down all your money on the Bulls, you should be aware that the current model doesn't account for certain external events such as... Derrick Rose tearing his ACL in the Bull's first game. The Bulls played great this year without Derrick in the lineup, but his absence is definitely going to hurt their chances...

Another surprise is the relatively low probabilities for the top teams of the season. Looking at the top 4 contenders, their cumulative probability of wining the title is barely over 50%. Again, this explains some of the regular surprises we see every now and again (every other year theoretically ;-) ).

There are many other caveats with this simple model, homecourt advantage is not taken into into account, nor is the fact that certain teams having already secured their playoff position rested their star players and lost games that were of no importance.

Nevertheless, I will try to continue improving the model and adress the current limitations. Naturally, I will also regularly post updated probabilities as the playoffs progress.

Now back to the replay of Kevin Durant's shot...